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Question

Mathematics Question on Double and triple integrals

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The integral (x2+y2+z2)dxdydz\int \int \int (x^2+y^2+z^2)dxdydz taken over the volume enclosed by the sphere x2+ y2+z2 = 1 is 4π5\frac{4\pi}{5}
Reason R: 0101x dxdy=12\int^{1}_{0}\int^{1}_{0}x\ dxdy=\frac{1}{2}
In the light of the above statements, choose the most appropriate answer from the options given below:

A

Both A and R are correct and R is the correct explanation of A

B

Both A and R are correct but R is NOT the correct explanation of A

C

A is correct but R is not correct

D

A is not correct but R is correct

Answer

Both A and R are correct but R is NOT the correct explanation of A

Explanation

Solution

The correct option is(B):Both A and R are correct but R is NOT the correct explanation of A.